Sobolev Space Regularised Pre Density Models

arXiv:2307.13763v2 Announce Type: replace-cross
Abstract: We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive bias of the model clear and interpretable. While there is no closed analytic form for the associated kernel, we show that one can approximate it using sampling. The optimization problem needed to determine the density is non-convex, and standard gradient methods do not perform well. However, …

abstract arxiv bias clear consistent cs.ai cs.lg form inductive kernel non-parametric norm parametric show space stat.ml type